Why does the surface of some lakes become concave just before the water falls over a weir?

Two words : adhesion and surface tension...

The deeper watermolecules will fall over first, then the top layers of the water. the reason for this is that the surface will always try to maintain or restore the original configuration once some perturbation has occured...
Think of what would happen if you would slowly move a ring out of water. the surface-layers will try to stick to the rings...they want the ring to stay in the water and thus maintain the original configuration. These things are used in experiments to measure the surface tension of fluids in general...